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That is completely false. Modelling the inside of the earth as a hollow spherical shell, the force inside at all points due to the gravity of the surrounding sh

by vecter 16y ago

That is completely false. Modelling the inside of the earth as a hollow spherical shell, the force inside at all points due to the gravity of the surrounding shell is 0.

ars 16y ago
But it's not actually a shell. In a solid sphere there is always force, and it always points to, and is lowest, at the center.
- vecter 16y ago
  I assumed the black hole carved out a spherical hole in the center of the Earth. If it was inside it, then it would be inside a spherical shell (a very thick one at that).
  - ars 16y ago
    But, you said it would be unstable, while actually if it crashed into the wall the resultant forces would put it back somewhere in the middle. Or more accurately oscillating back and forth in the middle, but not touching the wall. If there was any vapor in the middle (which seems likely to me, considering it would be a perfect vacuum at pretty extreme temperatures), then the gas would eventually slow down the oscillations and it would end up exactly in the middle.
    - joe_the_user 16y ago
      Well, it would be sucking up the matter on the walls as well.. BTW, Sci fans of yesteryear were disappointed when it was discovered that Dyson Spheres and Ring Worlds gravitationally unstable...
      - ars 16y ago
        > it would be sucking up the matter on the walls as well It won't. The first time it touches (or comes near) the wall it will take what it can get, but it will never go farther than that. There is nothing that will "push" it closer to the walls.
        jules 16y ago
        You are missing the crucial point. The force in a cave in the middle of the earth is ZERO, there is NO force directed to the center of the cave. This is not an intuitively correct statement, but if you carry out the calculation you will see that it is true. If you take a solid sphere and carve out a spherical cave in the center, then everywhere (not just in the center) inside this cave all the little forces from all the atoms of the big solid sphere cancel out. So this means that inside the cave the black hole will just move in one direction, until it hits the wall. Then it will suck up some mass and be pulled back to the center. Then it will suck up some mass on the other side, etc. The only way the black hole will remain in the cave is if you put it in the cave with exactly zero velocity to begin with. As soon as one atom falls into it it will start to eat up the earth.
        ars 16y ago
        No, I am not missing that point. You are missing a point. Yes, inside the cave there is no force. But the black hole can hit the wall just once. After that it can not go any farther. If passes thought/inside the wall it will be pulled back to the center, and the momentum exchange with the earth will slow it down (so next time it won't go as far). If it was just touching the wall, then that is as far as it can possibly go. So once it's inside it's little cave, it's done. It can't eat anymore. (Unless of course there is no cave and the earth feeds it, but we are assuming a cave.) You are missing three points: one is that if there is no cave, and it's oscillating through the earth, it will be pulled to the center. Two is that it looses momentum each time through the earth. And three is that once it's inside it's hollow cave it can no longer reach the wall.
        jules 16y ago
        I don't know what to say. On one hand you seem to agree that there is no force to slow the black hole down inside the cave, but on the other hand you claim that the black hole will remain inside the cave. > You are missing three points: one is that if there is no cave, and it's oscillating through the earth, it will be pulled to the center. Agreed. > Two is that it looses momentum each time through the earth. I'm not so sure about that. Mass is added to the black hole, and perhaps this causes the total momentum to increase. > And three is that once it's inside it's hollow cave it can no longer reach the wall. If it is stopped inside the cave. But there is no force to stop it.

by vecter 16y ago

That is completely false. Modelling the inside of the earth as a hollow spherical shell, the force inside at all points due to the gravity of the surrounding shell is 0.

ars 16y ago

But it's not actually a shell. In a solid sphere there is always force, and it always points to, and is lowest, at the center.

vecter 16y ago
I assumed the black hole carved out a spherical hole in the center of the Earth. If it was inside it, then it would be inside a spherical shell (a very thick one at that).
- ars 16y ago
  But, you said it would be unstable, while actually if it crashed into the wall the resultant forces would put it back somewhere in the middle. Or more accurately oscillating back and forth in the middle, but not touching the wall. If there was any vapor in the middle (which seems likely to me, considering it would be a perfect vacuum at pretty extreme temperatures), then the gas would eventually slow down the oscillations and it would end up exactly in the middle.
  - joe_the_user 16y ago
    Well, it would be sucking up the matter on the walls as well.. BTW, Sci fans of yesteryear were disappointed when it was discovered that Dyson Spheres and Ring Worlds gravitationally unstable...
    - ars 16y ago
      > it would be sucking up the matter on the walls as well It won't. The first time it touches (or comes near) the wall it will take what it can get, but it will never go farther than that. There is nothing that will "push" it closer to the walls.
      - jules 16y ago
        You are missing the crucial point. The force in a cave in the middle of the earth is ZERO, there is NO force directed to the center of the cave. This is not an intuitively correct statement, but if you carry out the calculation you will see that it is true. If you take a solid sphere and carve out a spherical cave in the center, then everywhere (not just in the center) inside this cave all the little forces from all the atoms of the big solid sphere cancel out. So this means that inside the cave the black hole will just move in one direction, until it hits the wall. Then it will suck up some mass and be pulled back to the center. Then it will suck up some mass on the other side, etc. The only way the black hole will remain in the cave is if you put it in the cave with exactly zero velocity to begin with. As soon as one atom falls into it it will start to eat up the earth.
        ars 16y ago
        No, I am not missing that point. You are missing a point. Yes, inside the cave there is no force. But the black hole can hit the wall just once. After that it can not go any farther. If passes thought/inside the wall it will be pulled back to the center, and the momentum exchange with the earth will slow it down (so next time it won't go as far). If it was just touching the wall, then that is as far as it can possibly go. So once it's inside it's little cave, it's done. It can't eat anymore. (Unless of course there is no cave and the earth feeds it, but we are assuming a cave.) You are missing three points: one is that if there is no cave, and it's oscillating through the earth, it will be pulled to the center. Two is that it looses momentum each time through the earth. And three is that once it's inside it's hollow cave it can no longer reach the wall.
        jules 16y ago
        I don't know what to say. On one hand you seem to agree that there is no force to slow the black hole down inside the cave, but on the other hand you claim that the black hole will remain inside the cave. > You are missing three points: one is that if there is no cave, and it's oscillating through the earth, it will be pulled to the center. Agreed. > Two is that it looses momentum each time through the earth. I'm not so sure about that. Mass is added to the black hole, and perhaps this causes the total momentum to increase. > And three is that once it's inside it's hollow cave it can no longer reach the wall. If it is stopped inside the cave. But there is no force to stop it.